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- W1966450417 abstract "Let K be a convex body in ℝd . It is known that there is a constant C 0 depending only on d such that the probability that a random copy ρ(K) of K does not intersect ℤd is smaller than $frac{C_{0}}{|K|}$ and this is best possible. We show that for every k<d there is a constant C such that the probability that ρ(K) contains a subset of dimension k is smaller than $frac{C}{|K|}$. This is best possible if k=d−1. We conjecture that this is not best possible in the rest of the cases; if d=2 and k=0 then we can obtain better bounds. For d=2, we find the best possible value of C 0 in the limit case when width(K)→0 and |K|→∞." @default.
- W1966450417 created "2016-06-24" @default.
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- W1966450417 date "2011-11-29" @default.
- W1966450417 modified "2023-09-22" @default.
- W1966450417 title "The Probability that a Convex Body Intersects the Integer Lattice in a k-dimensional Set" @default.
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- W1966450417 doi "https://doi.org/10.1007/s00454-011-9389-x" @default.
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